A present need exists for the development of accurate and efficient dose calculation methods for clinical treatment planning in external beam radiotherapy. Due to recent advances in image guided localization techniques and the development of more precise beam delivery methods such as Intensity Modulated Radiation Therapy (IMRT) and Stereotactic Radiosurgery (SRS), the potential exists to substantially reduce margins and improve dose conformity. However, most dose calculation methods in clinical use today employ approximations that limit their accuracy and scope of use, especially with narrow beams in the presence of heterogeneities. As a result, the adoption of more accurate methods such as Monte Carlo is seen as highly desirable. However, Monte Carlo calculations can be time consuming, limiting their effectiveness for clinical treatment planning. The application of a novel deterministic dose calculation method, which solves the differential form of the governing transport equations for neutral and charged particles is proposed. As indicated in preliminary studies, this approach has the potential to provide accuracy comparable to detailed Monte Carlo simulations with a substantially faster computational speed. The proposed approach incorporates anisotropic element adaptation to efficiently resolve complex anatomical features and sharp solution gradients, which is aided by the use of higher-order discontinuous finite element methods on variably sized tetrahedral elements. In Phase 1, a proof-of-concept process will be developed to quantify performance for patient specific dose calculations. This will be validated with detailed Monte Carlo results for selected treatment plans incorporating bone, air and lung heterogeneities, using both wide and narrow beams. Success will be measured on performance relative to Monte Carlo, defined in terms of combined speed and accuracy. Potential enhancements to further improve efficiency in Phase 2 will be identified, and an estimate of achievable clinical performance will be provided.